Temporary fix for wall collapse?

I've lived in my property for around 9 years and my neighbour around 4 and this is a problem that has always been there, but never addressed. My driveway is approx 7' higher than theirs and part of the retaining wall has collapsed and is leaning against their garage. Water has evidently been accumulating where my brickwork has been level to and touching the woodwork supporting the roof. My neighbour has (quite rightly, no dispute from my part) asked me to remove the brickwork in order to repair the damage and prevent the same happening again.

Today, I have removed all loose stone and bricks and this is what we're left with. My concern is that removing anything further will cause more damage than good, so I am after your opinions on how you would approach this.